Probabilistic models have been used to capture many features of
dynamic and uncertain environments. One of the simplest
probabilistic models for modeling change is the discrete-time, finite-state Markov model. In
this model, it is assumed that the state of the environment at time \(t\)  is dependent
only on the prior states going back to the \(t - k\)  time point, where \(k\)  is the order of the model (when \(k = 1\) , we have a first-order
Markov model). While this Markov assumption is violated by many natural
processes [1]}, it can still serve as a useful
idealization (or null model) in some
contexts. We chose to focus on this simple model in order to
better understand how biochemical circuits that perform
inference can be systematically derived from a probabilistic
model's description.
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